Dispensing devices in the form of hand-operated pumps for containers for fluids or dispensing valves for containers for fluids subjected to the pressure of propellant gas are known, which are assigned an auxiliary valve to let in fluid from a container which adopts an oblique or substantially reversed or upside-down position. In these conventional devices, the auxiliary valve consists of a ball valve which is assigned to the pump housing or valve housing of the dispensing device in question. The ball valve is mounted to be freely and reciprocally movable parallel to the axis between an open position and a closed position. It is exclusively subjected to gravity, so that the ball valve adopts its final position more or less quickly—or not at all—as a function of the oblique position of the container and of the viscosity of the liquid therein. This results, inter alia, in a nonuniform dispensing of the fluid in the container as a consequence of a differing admixing of air and is perceived by the consumer as disadvantageous. This disadvantage is particularly noticeable in the case of cosmetic or pharmaceutical products, where the consumer relies on dispensing a particular quantity of the product when actuating such dispenser packs.